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Correspondence, by Benedict de Spinoza, [1883], at sacred-texts.com
Dearest Friend,—I have received two letters from you, one dated Jan. 11, delivered to me by our friend, N. N., the other dated March 26, sent by some unknown friend to Leyden. They were both most welcome to me, especially as I gathered from them, that all goes well with you, and that you are often mindful of me. I also owe and repay you the warmest thanks for the courtesy and consideration, with which you have always been kind enough to treat me: I hope you will believe, that I am in no less degree devoted to you, as, when occasion offers, I will always endeavour to prove, as far as my poor powers will admit. As a first proof, I will do my best to answer the questions you ask in your letters. You request me to tell you, what I think about the infinite; I will most readily do so.
Everyone regards the question of the infinite as most difficult, if not insoluble, through not making a distinction between that which must be infinite from its very nature,. or in virtue of its definition, and that which has no limits, not in virtue of its essence, but in virtue of its cause; and also through not distinguishing between that which is called
infinite, because it has no limits, and that, of which the parts cannot be equalled or expressed by any number, though the greatest and least magnitude of the whole may be known; and, lastly, through not distinguishing between that, which can be understood but not imagined, and that which can also be imagined. If these distinctions, I repeat, had been attended to, inquirers would not have been overwhelmed with such a vast crowd of difficulties. They would then clearly have understood, what kind of infinite is indivisible and possesses no parts; and what kind, on the other hand, may be divided without involving a contradiction in terms. They would further have understood, what kind of infinite may, without solecism, be conceived greater than another infinite, and what kind cannot be so conceived. All this will plainly appear from what I am about to say.
However, I will first briefly explain the terms substance, mode, eternity, and duration.
The points to be noted concerning substance are these: First, that existence appertains to its essence; in other words, that solely from its essence and definition its existence follows. This, if I remember rightly, I have already proved to you by word of mouth, without the aid of any other propositions. Secondly, as a consequence of the above, that substance is not manifold, but single: there cannot be two of the same nature. Thirdly, every substance must be conceived as infinite.
The modifications of substance I call modes. Their definition, in so far as it is not identical with that of substance, cannot involve any existence. Hence, though they exist, we can conceive them as non-existent. From this it follows, that, when we are regarding only the essence of modes, and not the order of the whole of nature, we cannot conclude from their present existence, that they will exist or not exist in the future, or that they have existed or not existed in the past; whence it is abundantly clear, that we conceive the existence of substance as entirely different from the existence of modes. From this difference arises the distinction between eternity and duration. Duration is only applicable to the existence of modes; eternity is applicable to the existence of substance. that is, the infinite
faculty of existence or being (infinitum existendi sive (invitâ Latinitate 1) essendi fruitionem). From what has been said it is quite clear that, when, as is most often the case, we are regarding only the essence of modes and not the order of nature, we may freely limit the existence and duration of modes without destroying the conception we have formed of them; we may conceive them as greater or less, or may divide them into parts. Eternity and substance, being only conceivable as infinite, cannot be thus treated without our conception of them being destroyed. Wherefore it is mere foolishness, or even insanity, to say that extended substance is made up of parts or bodies really distinct from one another. It is as though one should attempt by the aggregation and addition of many circles to make up a square, or a triangle, or something of totally different essence. Wherefore the whole heap of arguments, by which philosophers commonly en' to show that extended substance is finite, falls to the ground by its own weight. For all such persons suppose, that corporeal substance is made up of parts. In the same way, others, who have persuaded themselves that a line is made up of points, have been able to discover many arguments to show that a line is not infinitely divisible. If you ask, why we are by nature so prone to attempt to divide extended substance, I answer, that quantity is conceived by us in two ways, namely, by abstraction or superficially, as we imagine it by the aid of the senses, or as substance, which can only be accomplished through the understanding. So that, if we regard quantity as it exists in the imagination (and this is the more frequent and easy method), it will be found to be divisible, finite, composed of parts, and manifold. But, if we regard it as it is in the understanding, and the thing be conceived as it is in itself (which is very difficult), it will then, as I have sufficiently shown you before, be found to be infinite, indivisible, and single.
Again, from the fact that we can limit duration and quantity at our pleasure, when we conceive the latter abstractedly
as apart from substance, and separate the former from the manner whereby it flows from things eternal, there arise time and measure; time for the purpose of limiting duration, measure for the purpose of limiting quantity, so that we may, as far as is possible, the more readily imagine them. Further, inasmuch as we separate the modifications of substance from substance itself, and reduce them to classes, so that we may, as far as is possible, the more readily imagine them, there arises number, whereby we limit them. Whence it is clearly to be seen, that measure, time, and number, are merely modes of thinking, or, rather, of imagining. It is not to be wondered at, therefore, that all, who have endeavoured to understand the course of nature by means of such notions, and without fully understanding even them, have entangled themselves so wondrously, that they have at last only been able to extricate themselves by breaking through every rule and admitting absurdities even of the grossest kind. For there are many things which cannot be conceived through the imagination but only through the understanding, for instance, substance, eternity, and the like; thus, if anyone tries to explain such things by means of conceptions which are mere aids to the imagination, he is simply assisting his imagination to run away with him. 1 Nor can even the modes of substance ever be rightly understood, if we confuse them with entities of the kind mentioned, mere aids of the reason or imagination. In so doing we separate them from substance, and the mode of their derivation from eternity, without which they can never be rightly understood. To make the matter yet more clear, take the following example: when a man conceives of duration abstractedly, and, confusing it with time, begins to divide it into parts, he will never be able to understand how an hour, for instance, can elapse. For in order that an hour should elapse, it is necessary that its half should elapse first, and afterwards half of the remainder, and again half of the half of the remainder, and if you go on thus to infinity, subtracting the half of the residue, you will never be able
to arrive at the end of the hour. Wherefore many, who are not accustomed to distinguish abstractions from realities, have ventured to assert that duration is made up of instants, and so in wishing to avoid Charybdis have fallen into Scylla. It is the same thing to make up duration out of instants, as it is to make number simply by adding up noughts.
Further, as it is evident from what has been said, that neither number, nor measure, nor time, being mere aids to the imagination, can be infinite (for, otherwise, number would not be number, nor measure measure, nor time time); it is hence abundantly evident, why many who confuse these three abstractions with realities, through being ignorant of the true nature of things, have actually denied the infinite.
The wretchedness of their reasoning may be judged by mathematicians, who have never allowed themselves to be delayed a moment by arguments of this sort, in the case of things which they clearly and distinctly perceive. For not only have they come across many things, which cannot be expressed by number (thus showing the inadequacy of number for determining all things); but also they have found many things, which cannot be equalled by any number, but surpass every possible number. But they infer hence, that such things surpass enumeration, not because of the multitude of their component parts, but because their nature cannot, without manifest contradiction, be expressed in terms of number. As, for instance, in the case of two circles, non-concentric, whereof one encloses the other, no number can express the inequalities of distance which exist between the two circles, nor all the variations which matter in motion in the intervening space may undergo. This conclusion is not based on the excessive size of the intervening space. However small a portion of it we take, the inequalities of this small portion will surpass all numerical expression. Nor, again, is the conclusion based on the fact, as in other cases, that we do not know the maximum and the minimum of the said space. It springs simply from the fact, that the nature of the space between two non-concentric circles cannot be expressed in number. Therefore, he who would assign a numerical equivalent
for the inequalities in question, would be bound, at the same time, to bring about that a circle should not be a circle.
The same result would take place—to return to my subject—if one were to wish to determine all the motions undergone by matter up to the present, by reducing them and their duration to a certain number and time. This would be the same as an attempt to deprive corporeal substance, which we cannot conceive except as existent, of its modifications, and to bring about that it should not possess the nature which it does possess. All this I could clearly demonstrate here, together with many other points touched on in this letter, but I deem it superfluous.
From all that has been said, it is abundantly evident that certain things are in their nature infinite, and can by no means be conceived as finite; whereas there are other things, infinite in virtue of the cause from which they are derived, which can, when conceived abstractedly, be divided into parts, and regarded as finite. Lastly, there are some which are called infinite or, if you prefer, indefinite, because they cannot be expressed in number, which may yet be conceived as greater or less. It does not follow that such are equal, because they are alike incapable of numerical expression. This is plain enough, from the example given, and many others.
Lastly, I have put briefly before you the causes of error and confusion, which have arisen concerning the question of the infinite. I have, if I mistake not, so explained them that no question concerning the infinite remains untreated, or cannot readily be solved from what I have said; wherefore, I do not think it worth while to detain you longer on the matter.
But I should like it first to be observed here, that the later Peripatetics have, I think, misunderstood the proof given by the ancients who sought to demonstrate the existence of God. This, as I find it in a certain Jew named Rabbi Ghasdai, runs as follows:—"If there be an infinite series of causes, all things which are, are caused. But nothing which is caused can exist necessarily in virtue of its own nature. Therefore there is nothing in nature, to whose essence existence necessarily belongs. But this is
absurd. Therefore the premise is absurd also." Hence the force of the argument lies not in the impossibility of an actual infinite or an infinite series of causes; but only in the absurdity of the assumption that things, which do not necessarily exist by nature, are not conditioned for existence by a thing, which does by its own nature necessarily exist.
I would now pass on, for time presses, to your second letter: but I shall be able more conveniently to reply to its contents, when you are kind enough to pay me a visit. I therefore beg that you will come as soon as possible; the time for travelling is at hand. Enough. Farewell, and keep in remembrance Yours, &c.
Rhijnsburg, 20 April, 1663.
317:1 See Introduction, pp. xv, xx.
319:1 Spinoza apologizes here in the original for the use of the unclassical form "essendi," being. The classical Latin verb of being is, as the ancients themselves admitted, defective in a most inconvenient degree.
320:1 "Nihilo plus agit, quam si det operam ut sua imaginatione insafiat." Mr. Pollock paraphrases, "It is like applying the intellectual tests of sanity and insanity to acts of pure imagination."